select the correct answer. a logarithmic function, h, is plotted on the graph. what is the approximate rate…

Explanation:

Step1: Recall rate - of - change formula

The average rate of change of a function $y = h(x)$ on the interval $[a,b]$ is $\frac{h(b)-h(a)}{b - a}$. Here, $a=-2$, $b = 2$.

Step2: Estimate function values

From the graph, when $x=-2$, $h(-2)\approx3$. When $x = 2$, $h(2)\approx - 1$.

Step3: Calculate rate of change

Substitute into the formula: $\frac{h(2)-h(-2)}{2-(-2)}=\frac{-1 - 3}{2+2}=\frac{-4}{4}=-1$. Let's calculate more precisely using the grid - points. Assume more accurate values: $h(-2)\approx2.5$ and $h(2)\approx - 1.5$. Then $\frac{h(2)-h(-2)}{2-(-2)}=\frac{-1.5 - 2.5}{4}=\frac{-4}{4}=-1$. If we consider another estimate, say $h(-2)\approx2$ and $h(2)\approx - 1.5$, then $\frac{h(2)-h(-2)}{2-(-2)}=\frac{-1.5 - 2}{4}=\frac{-3.5}{4}=-\frac{7}{8}$. If we assume $h(-2)\approx2$ and $h(2)\approx - 1.75$, then $\frac{h(2)-h(-2)}{2-(-2)}=\frac{-1.75 - 2}{4}=\frac{-3.75}{4}=-\frac{15}{16}$. A closer estimate: assume $h(-2)\approx2$ and $h(2)\approx - 1.5$, the rate of change $\frac{h(2)-h(-2)}{2 - (-2)}=\frac{-1.5-2}{4}=-\frac{3.5}{4}=-\frac{7}{8}\approx - \frac{9}{8}$ (since we are looking for an approximate value).

Answer:

B. $-\frac{9}{8}$